I don't know the answer to your question, but I do know that one of your assumptions is incorrect. The reason for making gmail invitation-only was NOT to build

I don't know the answer to your question, but I do know that one of your assumptions is incorrect. The reason for making gmail invitation-only was NOT to build a graph and keep nodes artificially small. Rather, the goal was to provide a way of ramping up usage in a controlled manner. By throttling the number of invites given out, Google could control the rate at which new people signed up for the service and make sure that there were always enough servers available to handle the load so the experience for existing users wasn't degraded. They are currently doing the exact same thing with accounts for Google Wave. In this case, there is an added benefit: unless you know someone else who has a wave account, having one is of absolutely no use because you have no one to communicate with.